1. Field of the Invention
The invention disclosed herein relates to subterranean imaging and, in particular, to arrangements of electrodes for resistivity imaging within a wellbore.
2. Description of the Related Art
Imaging of formations surrounding boreholes provides valuable information for describing geologic features. Some of the features include structural framework, fracture patterns, sedimentary feature, and in-situ stress orientation. High-resolution borehole images are used as an aid in providing conventional core description and determining orientation. While various technologies are used for imaging, one technology that is particularly useful involves resistivity measurements.
Information obtained by performing resistivity measurements is useful for planning formation testing, sampling, perforating and other such tasks. For thinly laminated turbidite sands and other sequences, these images are often one of the few practical methods for determining net sand and deposit thicknesses.
One instrument for making resistivity measurements is available from Baker Hughes, Incorporated of Houston, Tex. The instrument, referred to as an “Earth Imager,” has provided for a variety of resistivity images.
Reference may be had to FIG. 1. In FIG. 1, there is shown a depiction of the prior art instrument for performing resistivity imaging. In this example, the instrument 20 is disposed within a wellbore 11. The instrument 20 includes pads 3 mounted on articulating arms 2. The articulated pads 3 are typically pressed up against a wall of the wellbore 11 and make firm contact therewith. Current I flows from the return electrode 4 to the pads 3. The return electrode 4 is electrically separated from each of the pads 3 by an isolator 5.
In the prior art instrument, each pad 3 contains a set of eight measuring sensor electrodes surrounded by a metal pad housing which acts as a focusing electrode for the measuring sensor electrodes. FIG. 2 provides a simplified illustration of the prior art pad 3 and sensor electrodes 8 disposed on a face of the pad 3. As shown in FIG. 2A, each of the sensor electrodes 8 has a generally rectangular appearance. As is typically the case, the sensor electrodes 8 are disposed in an array (in this case, the array having eight elements). An exemplary response function for three of the sensor electrodes 8 is provided in FIG. 2B.
During operation of the instrument, current measurement for each measuring sensor electrode 8 is a function of the formation conductivity and the voltage applied. High resolution images are achieved by sampling at a high rate (for example, about 120 samples per foot), using the readings from the forty eight sensor electrodes 8 mounted on the six pads 3.
These measurements are scaled to resistivity values so that they can be correlated with conventional shallow measurements. All forty eight curves acquired are corrected for speed variations and oriented to true North using magnetometer and accelerometer readings from a separate orientation instrument prior being presented as a color scaled resistivity image.
While this instrument produces valuable data, one skilled in the art of data interpretation may recognize certain limitations. For example, in certain conditions, aliasing of data occurs. That is, when a continuous signal is reconstructed from the samples, the result may be one of the aliases, which represents a form of distortion. The term “aliasing” therefore refers to ambiguity created by sampling or the subsequent distortion or both.
Aliasing may arise from a variety of sources. One skilled in the art will recognize that the shape of the sensor electrodes 8 depicted in FIG. 2 is one such source. For example, development of image results for areas between the sensor electrodes 8 may inherently involve aliasing. More specifically, with reference to FIG. 2B, an exemplary response function for the array of sensor electrodes 8 is shown. As there is a portion of the pad 3 between each sensor electrode 8, no data is collected in this area (strictly speaking, and without regard for edge effects and other such phenomena).
In the art of digital imaging, effects from aliasing and other design limitations are known. Various techniques for improved performance have been presented. Reference may be had to the article entitled “Smart CMOS Image Sensor Arrays,” by Schanz et al., and published in IEEE transactions on Electron Devices, Vol. 44, No. 10, October 1997. This article discusses, among other things, implementation of smart image sensor arrays.
Therefore, what are needed are designs for sensor electrodes that reduce or eliminate the effect of aliasing on resistivity images.